There are code-based cryptographic primitives whose security relies precisely on the difficulty of decoding at the Gilbert-Varshamov relative distance (something which is also called full distance decoding [1]}, [2]}), for instance the Stern code-based identification schemes or associated signatures schemes [3]}, [4]}, [5]}, [6]}. In the light of the upcoming NIST second call for new quantum resistant signature algorithms, it is even more important to have a stable and precise assessment of what we may expect about the complexity of solving this problem. For much smaller distances, say sub-linear, which is relevant for cryptosystems like [7]}, [8]}, the situation seems much more stable/well understood, since the complexity exponent of all the above-mentioned algorithms is the same in this regime [9]}.
